a dog's chance一般用于否定句中，意思是“渺茫的机会；极微小的机会”。

【例句】
You are confronted with a very powerful team. I'm afraid you won't have a dog's chance to win the game today.
你们今天要打的是一个很有实力的队，恐怕你们没机会赢了。

A failure in life doesn't mean that you just have a dog's chance.
生活中的一次失败并不意味着你就再也没有机会了。